David W. answered • 08/22/16
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Mean, median, and mode are measures of "central tendency." They give us an overall indication of what a population looks like.
It also helps to know values of range, standard deviation, variance, etc. Those tell us how "spread out" the values are.
If we consider any diverse group of observations, we might prefer the median to the mean. For example,
With 10,000 people, the mean salary might be $45,000, but the range is $20,000 to $3,000,000 with a mean of $100,000.
In that situation, "outliers" have drastically affected the mean. The few people that earn a lot of money have distorted the overall average (mean). It is better to get the "half-way point" (median). Even the mode (the "most frequent") does not necessarily represent the population, since it could be $25,000, for example.
Some more examples:
grades on a test
height of students (some of whom are on basketball team)
age of employees in a company
... (you can think of a lot more -- diverse is the key).
Often, when collecting statistics, "outliers" are discarded as either typos or invalid observations. For example, if you have collected a set of high temperatures for the month (like 70, 74, 768, 73, ...), you should consider the temperature of 768 to be invalid.
Note that ANY changes to raw observations is strictly governed by the rules of statistics. There are usually procedures for processing "missing values," or "invalid values," etc.
